The Representation of Fuzzy Algorithms

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Description/Abstract

This paper will compare two apparently different approaches for representing fuzzy algorithms: discrete and continuous. Traditionally, fuzzy algorithms have been implemented using a discrete approach where the fuzzy sets that form the rule base are defined at a set of discrete points. However, continuous fuzzy systems have recently gained in popularity, partly due to their links with certain classes of neural networks, but also because they generally require a smaller number of parameters and have a reduced computational cost. The paper will discuss the role of the fuzzy sets and the fuzzy operators and arguments are made for adopting continuous rather than discrete membership functions and algebraic rather than truncation operators. It is also shown that using algebraic operators in conjunction with a centre of gravity defuzzification strategy reduces fuzzy composition and defuzzification to a single operation and this allows the effect of different fuzzy input representations to be investigated.